Mister Exam

Other calculators


9*x*e^(3*x)

Integral of 9*x*e^(3*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |       3*x   
 |  9*x*e    dx
 |             
/              
0              
$$\int\limits_{0}^{1} 9 x e^{3 x}\, dx$$
Integral(9*x*E^(3*x), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. There are multiple ways to do this integral.

        Method #1

        1. Let .

          Then let and substitute :

          1. The integral of a constant times a function is the constant times the integral of the function:

            1. The integral of the exponential function is itself.

            So, the result is:

          Now substitute back in:

        Method #2

        1. Let .

          Then let and substitute :

          1. The integral of a constant times a function is the constant times the integral of the function:

            1. The integral of a constant is the constant times the variable of integration:

            So, the result is:

          Now substitute back in:

      Now evaluate the sub-integral.

    2. The integral of a constant times a function is the constant times the integral of the function:

      1. Let .

        Then let and substitute :

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of the exponential function is itself.

          So, the result is:

        Now substitute back in:

      So, the result is:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                                  
 |      3*x           3*x        3*x
 | 9*x*e    dx = C - e    + 3*x*e   
 |                                  
/                                   
$$\left(3\,x-1\right)\,e^{3\,x}$$
The graph
The answer [src]
       3
1 + 2*e 
$$9\,\left({{2\,e^3}\over{9}}+{{1}\over{9}}\right)$$
=
=
       3
1 + 2*e 
$$1 + 2 e^{3}$$
Numerical answer [src]
41.1710738463753
41.1710738463753
The graph
Integral of 9*x*e^(3*x) dx

    Use the examples entering the upper and lower limits of integration.